[Dune-devel] [GSoC2016]B-Spline geometry - current progress

[Oliver Sander]

Hi Xinyun,

thanks for your work.  I am currently travelling, but I'll have a look at your code when I get back
(thursday).  It would help me reviewing if you could post merge request for your individual changes.
Modifying the basis function calculation seems like a good idea that should definitely be merged,
provided the code is well done.

> My doubts 
> 1. How to implement the following functions?
> ctype volume() const.
> LocalCoordinate local(const GlobalCoordinate&) const;
> I don't know how to define the volume of the B-Spline structure and the inverse mapping from the physical space to the element space also seems non-trivial.

These two are the main challenge.  For the volume you will need some sort of numerical
integration.  Same with the 'local' method, where you will need a nonlinear equation solver.

> 2. Matrix operation
> I will need the transpose and pseudo-inverse of a matrix. I think these functions should already been implemented in DDUNE. I had a quick look of the FieldMatrix class but not sure if it is enough.

As far as I know these methods do not exist in Dune, and you will to write them yourself.

Best,
Oliver

> 
> Thanks for your time in advance.
> 
> Best regards,
> Xinyun 
> 
> 
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